3. Examples. Justify your answers briefly. (a) Give an example of a metric on R². (b) Is the set of all points (x, y) in R² such that y = x² sequentially compact? Explain why or why not. (c) Verify that the product of the Dedekind cut for 2 and that for 3 is the Dedekind cut for 6. (d) Explain why a strictly decreasing function is injective.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3.
Examples. Justify your answers briefly.
(a) Give an example of a metric on R².
(b) Is the set of all points (x, y) in R² such that y = x² sequentially compact?
Explain why or why not.
(c) Verify that the product of the Dedekind cut for 2 and that for 3 is the
Dedekind cut for 6.
(d) Explain why a strictly decreasing function is injective.
Transcribed Image Text:3. Examples. Justify your answers briefly. (a) Give an example of a metric on R². (b) Is the set of all points (x, y) in R² such that y = x² sequentially compact? Explain why or why not. (c) Verify that the product of the Dedekind cut for 2 and that for 3 is the Dedekind cut for 6. (d) Explain why a strictly decreasing function is injective.
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